More lift = more air into the engine and more exhaust out.
Engines are air pumps.
The more oxygen you can get in, and mixed with the correct amount of fuel, the more horsepower you will make.
Simple as that.
It's duration that has the biggest effect on your engines charactoristics.
You must establish what you want to do with your car before choosing camshafts.
Drag racing, Drift,Circuit Racing, Street/Strip etc.
Duration is the key word here.
EG: 220deg duration @ 0.050 is a small camshaft that would work well in street applications.
Useable power range normally 2500-3000 rpm to 6000 rpm.
300deg duration @ 0.050 is a cranky piece of gear, application Drag Racing.
Useable power range normally 4000 - 5000 rpm to 9000 rpm.
Above mentioned examples are NOT exact figures but are stated to give you an idea.
You can have a camshaft/s with 9.5mm of lift and 220 deg duration for street.
You can have a more aggresive camshaft/s ground with 9.5mm lift and 260 deg duration,this camshaft will make more horsepower but at a higher rpm.
Camshaft selection also comes back to engine hardware.
11 mm lift 300 deg duration on an engine with stock internals and standard turbo charger is pointless.
What do you want to do with your car,what is done to your engine.
I have made 625 hp @ the wheels with a customers car using only Tomie Pon Cams, but had the engine and turbo charger to support such a figure.
I know that if i want more horsepower with that combination i need more lift and duration and another set of springs.
However this is a street car and the owner dosnt want to sacrifice drivability.
So lift increase with no duration change = small/ marginal performance gain.
Lift increase with duration increase = more gain in power.